Jack Taylor scored 138 points for Grinnell College in their 179-104 victory over Faith Baptist College. He made a total of 59 baskets consisting of two-pointers, three-pointers, and free throws.

Question

The number of two point shots Jack made was four more than three times the number of free throws he made. How many three point shots he made, and how many free throws he made in this particular game.

Answer 1

This is a system of simultaneous equations in three unknown variables x (free throws / one-pointers), y (two-pointers) and z (three-pointers).

Jack Taylor scored 138 points

(1) 1x + 2y + 3z = 138

He made a total of 59 baskets consisting of two-pointers, three-pointers, and free throws

(2) x + y + z = 59

number of two point shots Jack made was four more than three times the number of free throws he made

(3) y = 3x + 4

We can eliminate y in both (1) and (2) by substituting the value of y from (3) to get:

1x + 2(3x + 4) + 3z = 138

=> 1x + 6x + 8 + 3z = 138

=> (4) 7x + 3z = 130

and x + (3x + 4) + z = 59

=> x + 3x + 4 + z = 59

=> (5) 4x + z = 55

Now we have two equations with only two unknowns (x and z) which we can now solve.

Let's multiply (5) by 3 to get 3z (in both), and then subtract from (4) as follows

7x + 3z = 130

-

12x + 3z = 165

=

-5x + 0z = -35

=> x = 7

Substitute x in (5) to get 4(7) + z = 55 => z = 55 - 28 = 27

With x and z found, substitute in initial equation (2) so 7 + y + 27 = 59

=> y = 59 - 34 = 25

Is the solution correct? Substitute all values in original equations, so 1(7) + 2(25) + 3(27) = 7 + 50 + 81 = 138 as required, and 7 + 25 + 27 = 59 as required, and 3(7) + 4 = 25 as required.

Hence... How many three point shots? 27 & How many free throws? 7